Elliptic curve isogeny class with Cremona label 266910i (LMFDB label 266910.i)

• Label: 266910i
• Number of curves: $2$
• Conductor: $266910$
• CM: no
• Rank: $2$

Elliptic curves in class 266910i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
266910.i2	266910i1	$[1, 1, 0, -2452, 141916]$	$-1631405145996361/7882185937500$	$-7882185937500$	$[2]$	$761856$	$1.1592$	$\Gamma_0(N)$-optimal
266910.i1	266910i2	$[1, 1, 0, -58702, 5440666]$	$22371441369258096361/43635080711250$	$43635080711250$	$[2]$	$1523712$	$1.5057$

Rank

The elliptic curves in class 266910i have rank $2$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$3$	$1 + T$
$5$	$1 - T$
$7$	$1 + T$
$31$	$1 - T$
$41$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$13$	$1 - 2 T + 13 T^{2}$	1.13.ac
$17$	$1 - 2 T + 17 T^{2}$	1.17.ac
$19$	$1 + 6 T + 19 T^{2}$	1.19.g
$23$	$1 + 4 T + 23 T^{2}$	1.23.e
$29$	$1 - 10 T + 29 T^{2}$	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 266910i do not have complex multiplication.

Modular form 266910.2.a.i

Isogeny matrix

The $i,j$ entry is the smallest degree of a cyclic isogeny between the $i$-th and $j$-th curve in the isogeny class, in the Cremona numbering.

$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.